A233124 Number of n X 3 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

3, 80, 2688, 96256, 3497984, 127533056, 4653056000, 169793814528, 6196127858688, 226111237652480, 8251342992703488, 301111464108752896, 10988286523845115904, 400989192448372637696, 14633067014086637649920

Offset

1,1

Comments

Column 3 of A233129.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 48*a(n-1) - 448*a(n-2) + 1024*a(n-3).

Conjectures from Colin Barker, Mar 19 2018: (Start)

G.f.: x*(3 - 64*x + 192*x^2) / ((1 - 8*x)*(1 - 40*x + 128*x^2)).

a(n) = 8^(-1+n) + ((20-4*sqrt(17))^n*(-3+sqrt(17)) + (3+sqrt(17))*(4*(5+sqrt(17)))^n) / (32*sqrt(17)).

(End)

Example

Some solutions for n=4:
..0..1..0....0..1..5....0..1..5....0..1..2....0..1..2....0..1..5....0..1..2
..2..5..2....2..0..4....4..5..2....1..2..1....4..3..5....2..5..2....3..0..1
..0..1..5....5..2..5....0..3..4....3..0..3....2..0..2....0..4..0....1..3..0
..3..5..4....1..5..4....3..1..2....0..3..5....0..3..5....1..0..1....3..4..2

Crossrefs

Cf. A233129.

Sequence in context: A327250 A197248 A183265 * A251694 A355626 A274567

Adjacent sequences: A233121 A233122 A233123 * A233125 A233126 A233127

Keyword

nonn

Author

R. H. Hardin, Dec 04 2013

Status

approved